>The intent of that quote is to say “consciousness is subjective experience”

I doubt Nagel would go out of his way to offer such an unnatural linguistic construction, and other philosophers would adopt this construction as a standard point of reference, if that was the sole intent.

>So then are you saying there is no such thing as consciousness?

No, not at all. I'm only saying that if we want to talk about "the consciousness of a bat", we should talk about it directly, and not invent (implicitly) a second concept that is in some senses distinct from it, and in some sense comparable to it.